In many of the EU/Legends works, after Palpatine's death the Empire fragmented, many systems/sectors controlled by various Imperial officers turned warlords- is the First Order one faction of many or are all Imperials loyal to it?
TFA Visual Dictionary has this to say:
The Galactic Concordance defanged the Empire's ability to wage war, with strict disarmament treaties and punishing reparations. The Old Empire withered away, becoming a remnant of political hardliners locked in a cold war with the New Republic, before eventually breaking away to reform in the Unknown Regions as the mysterious First Order.
This sounds like First Order controls all of Galactic Empire's remaining supporters (in other words, no other Imperial factions).
Obviously, they don't control all of Galactic Empire's old territory, or old population:
Hux was a child when the Empire surrendered to the New Republic with the signing of the Galactic Concordance. His father fled the Academy on Arkanis, and was one of the Imperials to make the exodus into the Unknown Regions, which the Empire had secretly begun exploring. Hux grew up hearing legends of great Imperials, and how the Empire saved the galaxy from the violence of the Clone Wars.